where \(n_{i}\)  is equal to \(N_{i}\)  for bosons and \(N_{i}/2\)  for fermions, with \(N_i\)  already given in section .
\(\Delta M_{i}^{2}\left(\Phi _{*}\right)\)  is the difference of the field-dependent squared masses between the symmetric and broken phases.
According to \(\alpha _{\infty }\) , the phase transition can be divided into two cases [1]}:
